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Suppose Davidson goes hiking in the swamp and is struck and killed
by a lightning bolt. At the same time, nearby in the swamp another
lightning bolt spontaneously rearranges a bunch of molecules such that,
entirely by coincidence, they take on exactly the same form that
Davidson's body had at the moment of his untimely death.

This being, whom Davidson terms 'Swampman', has, of course, a brain
which is structurally identical to that which Davidson had, and will
thus, presumably, behave exactly as Davidson would have. He will walk
out of the swamp, return to Davidson's office at Berkeley, and write
the same essays he would have written; he will interact like an
amicable person with all of Davidson's friends and family, and so forth. - Is Davidson the same after as before?

Why do we ask these questions? Who cares if Davidson is the same or different on some metaphysical level? I don't care if a tree falls or a cat dies in a box. The point is always the same, there is no answer. These thought experiments aren't experiments at all. So why do they continually pop up? Does the floating man in the air without any sensory information have an identity? I'll think about your experiment when you successfully suspend me in the air. Actually, I might fly off without answering. I don't care much for riddles.

There are two answers to the question above, yes or no. They are both right and they are both wrong and they are both obsolete. It's an impossible and as such should we even think about it? Well, maybe still. Thought experiments are mostly just demonstrations of our faulty networking. They provide us with hints and scenarios so we can reassess what we think we already know. Hypothetical situations are great teaching tools.

So can we then set our brains to thinking about the one above (titled Swampman) It's a question of identity. But is it a question of the brain or the body? I think it should be more than just the rearranging of atoms that makes Davidson different. After all we tirelessly exchange old atoms for new ones our entire lives and even in just a few days the atomic make-up of your heart will be different than it is now. The creator of this thought experiment concludes that Davidson is different even though there is no discernible evidence of that difference. What this ignores though is that from one word to the next in writing this I am different too. We are constantly shifting both our mental and physical chemistry so much that I think the question is rendered mute.

Does anyone else have any good thought experiments or want to respond to this one? Or else have any reasons that we should obviate all of them from our consciousness?

It seems that the thought experiment can be purely a form of exercise and also a heuristic activity with an aim in mind. What about the specifics of a thinking method? Is that not on the same level of importance as the provocative question?

Everything is a thought experiment. What they reveal is the place of deliberation, not of decision. You don't care if a tree falling in the woods makes a sound or not, but the thought process, the question, that is what matters. One which I particularly like is I think from a Woody Allen movie which starts with the question: there is a burning library with the last remaining examples of Shakspeare's works. You run to save them but there is an old lady in the library, and you can either save her or the books not both - which do you save?

It is a stupid question you might say, but what's nice is what it opens up. In how it opens the moral question and how it frames it in a way which you can't run away from. You're there and you need to decide. Of course you don't need to decide, and you can't decide, but it still has an effect. It has an effect because you do decide and it's a daily decision of how you live your life, who you vote for, and what you support. Every day you decide on whether to save the old lady or the books, only several levels removed from that decision (like a prime minister ordering to go to battle knows people will be killed even if they are not the ones pulling the trigger).

On the other hand, the single most important thing to understand about philosophy (and life) is how important is the question you choose to face. The wrong questions (stupid thought experiments like you mention) will lead you nowhere. Choosing the correct question is the first step, and without the correct direction you can walk and walk and walk and it will lead you nowhere.

So yes, you should always be suspicious of the questions and roads people want you to take. Is this really the question we should be asking? That's where analytic philosophy mostly gets it wrong (though it depends of course). The moment you enter into their domain the fight is already lost. (You are drowned in senseless mind games which is like full gas in neutral.)

Ps. Actually having studied with Davidson in Berkeley, obviously jokes about the swampman and are we talking to him were "surprisingly" prevalent in class.